Five-card and protocol in committed format using only practical shuffles

In card-based cryptography, designing AND protocols in committed format is a major topic of research. The state-of-the-art AND protocol proposed by Koch,Walzer, and Härtel in ASIACRYPT 2015 uses only four cards, which is the minimum permissible number. Their protocol's minimality relies on somewhat complicated shuffles having non-uniform probabilities of possible outcomes. Restricting the allowed shuffles to "practical" ones, namely uniform closed shuffles, to our knowledge, six cards are sufficient: The sixcard AND protocol proposed by Mizuki and Sone in 2009 utilizes the random bisection cut, which is a uniform and cyclic (and hence, closed) shuffle. Thus, a question has arisen: Can we improve upon this six-card protocol using only practical shuffles? In other words, whether there exists a five-card AND protocol in committed format using only uniform closed shuffles has been one of the most important open questions in this field. In this paper, we answer the question affirmatively by designing a five-card committed-format AND protocol using only practical shuffles. The shuffles that our protocol uses are random cut and random bisection cut, both of which are uniform cyclic shuffles and can be easily implemented by humans.